order (of a ring)
The order of a ring $R$ is the order (http://planetmath.org/OrderGroup) of its additive group^{}, i.e. (http://planetmath.org/Ie) the number of elements of $R$. The order of $R$ can be denoted as $R$. If $R$ is finite, then $R$ is said to be a finite ring.
This definition of order is not necessarily standard. Please see http://planetmath.org/?op=getobj&from=corrections&id=12149this correction and the posts attached to it for more details.
This definition of order is used in the following works:

1.
Angerer, Josef and Pilz, Günter. “The Structure of Near Rings of Small Order.” Computer Algebra: EUROCAM ’82, European Computer Algebra Conference; Marseilles, France, April 1982. Editors: Goos, G. and Hartmanis, J. Berlin: SpringerVerlag, 1982, pp. 5764.

2.
Buck, Warren. http://planetmath.org/?op=getobj&from=papers&id=336Cyclic Rings. Charleston, IL: Eastern Illinois University, 2004.

3.
Fine, Benjamin. “Classification of Finite Rings of Order ${p}^{2}$.” Mathematics Magazine, vol. 66 #4. Washington, DC: Mathematical Association of America, 1993, pp. 248252.

4.
Fletcher, Colin R. “Rings of Small Order.” The Mathematical Gazette, vol. 64 #427. Leicester, England: The Mathematical Association, 1980, pp. 922.

5.
Lam, TsiYuen. A First Course in Noncommutative Rings. New York: SpringerVerlag, 2001.

6.
Mitchell, James. School of Mathematics and Statistics: MT4517 Rings and Fields, Lecture Notes 1. St. Andrews, Scotland: University of St. Andrews, 2006. URL: http://wwwhistory.mcs.stand.ac.uk/ jamesm/teaching/MT4517/MT4517notes1.pdfhttp://wwwhistory.mcs.stand.ac.uk/ jamesm/teaching/MT4517/MT4517notes1.pdf

7.
Nöbauer, Christof. Numbers of rings on groups of prime power order. Linz, Austria: Johannes Kepler Universität Linz. URL: http://www.algebra.unilinz.ac.at/ noebsi/ringtable.htmlhttp://www.algebra.unilinz.ac.at/ noebsi/ringtable.html

8.
Schwabe, Eric J. and Sutherland, Ian M. “Efficient Mappings for ParityDeclustered Data Layouts.” Computing and Combinatorics: 9th Annual International Conference, COCOON 2003; Big Sky, MT, USA, July 2003; Proceedings. Editors: Warnow, Tandy and Zhu, Binhai. Berlin: SpringerVerlag, 2003, pp. 252261.
Title  order (of a ring) 

Canonical name  OrderofARing 
Date of creation  20130322 17:10:31 
Last modified on  20130322 17:10:31 
Owner  Wkbj79 (1863) 
Last modified by  Wkbj79 (1863) 
Numerical id  15 
Author  Wkbj79 (1863) 
Entry type  Definition 
Classification  msc 1601 
Synonym  order 
Synonym  order of a ring 
Related topic  OrderGroup 
Defines  finite ring 